Step 1: Determine a confidence interval for the population proportion

The sample proportion is an estimate of the population proportion.Because the proportion is based on sample data and not on the entire population, it is unlikely that the sample proportion equals the population proportion. To better estimate the population proportion, use the confidence interval.

The confidence interval provides a range of likely values for the population proportion. For example, a 95% confidence level indicates that if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population proportion. The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size. For more information, go to Ways to get a more precise confidence interval.

The interval plot shows the confidence interval for the sample proportion with a reference line that indicates the hypothesized proportion.

Descriptive Statistics

N

Event

Sample p

95% CI for p

1000

87

0.087000

(0.070268, 0.106208)

Key Results: Sample p, 95% CI for p, Interval Plot

In these results, the estimate of the population proportion for households that made a purchase is 0.087. You can be 95% confident that the population proportion is between approximately 0.07 and 0.106.

To determine whether the difference between the population proportion and the hypothesized proportion is statistically significant, compare the p-value to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.

P-value ≤ α: The difference between the proportions is statistically significant (Reject H0)

If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis. You can conclude that the difference between the population proportion and the hypothesized proportion is statistically significant. Use your specialized knowledge to determine whether the difference is practically significant. For more information, go to Statistical and practical significance.

P-value > α: The difference between the proportions is not statistically significant (Fail to reject H0)

If the p-value is greater than the significance level, the decision is to fail to reject the null hypothesis. You do not have enough evidence to conclude that the difference between the population proportion and the hypothesized proportion is statistically significant. You should make sure that your test has enough power to detect a difference that is practically significant. For more information, go to Increase the power of a hypothesis test.

Test

Null hypothesis

H₀: p = 0.065

Alternative hypothesis

H₁: p ≠ 0.065

P-Value

0.0085

Key Result: P-Value

In these results, the null hypothesis states that the proportion of households that bought a new product equals 6.5%. Because the p-value is 0.0085, which is less than the significance level of 0.05, the decision is to reject the null hypothesis and conclude that the population proportion of households that bought the new product is different from 6.5%.